GATE MA study guide
GATE MA · Work through your exam, one topic at a time.
GATE 2026 is a national-level examination that assesses candidates on undergraduate-level subjects across Engineering, Technology, Science, Commerce, Arts, Architecture and Humanities. It is being organised by IIT Guwahati, working in collaboration with IISc Bengaluru and the other 22 IITs on behalf of the National Coordination Board, Department of Higher Education, Ministry of Education, Government of India. The GATE MA study guide has 11 sections and about 2,960 words.
01Linear Algebra
GATE MA's Linear Algebra section tests vector spaces over R and C, linear transformations, matrix canonical forms, and inner-product geometry. Expect numerical rank and eigenvalue problems plus short proofs.
265 words, about 1 min02Complex Analysis
Complex Analysis in GATE MA covers analytic functions, contour integration, series expansions, and residue calculus. Questions often combine a quick residue computation with a theorem such as Liouville or the maximum modulus principle.
281 words, about 1 min03Real Analysis
Real Analysis tests limits, continuity, integration, and convergence in metric spaces. GATE MA favors counterexamples: pointwise versus uniform convergence, and when limit operations commute.
287 words, about 1 min04Ordinary Differential Equations
Ordinary Differential Equations in GATE MA emphasizes solution techniques, existence–uniqueness, and qualitative behavior. Expect first-order equations, constant-coefficient linear systems, Laplace transforms, and Sturm–Liouville theory.
239 words, about 1 min05Partial Differential Equations
Partial Differential Equations in GATE MA covers first-order characteristics, classification of second-order equations, and the classical wave, heat, and Laplace equations, usually via separation of variables and Fourier series. First-order quasilinear: a(x,y,u)u x+b(x,y,u)u y=c(x,y,u); solve the characteristic system dx/a=dy/b=du/c.
247 words, about 1 min06Algebra
Algebra in GATE MA tests group theory (Lagrange, normal subgroups, Sylow) and ring theory (ideals, polynomial rings, fields). Problems are often short proofs or classification of small-order groups.
300 words, about 2 min07Functional Analysis
Functional Analysis in GATE MA covers normed and Banach spaces, Hilbert spaces, bounded operators, and the four big theorems. Expect norm computations, dual-space arguments, and compactness questions.
267 words, about 1 min08Numerical Analysis
Numerical Analysis in GATE MA tests interpolation, numerical integration, root finding, linear-system solvers, and numerical ODE methods, with emphasis on error orders and convergence. Lagrange interpolation through n+1 points has error f^{(n+1)}(ξ)/(n+1)!
259 words, about 1 min09Calculus of Variations
Calculus of Variations in GATE MA asks for extremals of integral functionals, boundary conditions, and second-order sufficiency. Typical problems involve geodesics, isoperimetric constraints, and Rayleigh–Ritz approximations.
249 words, about 1 min10Linear Programming
Linear Programming in GATE MA covers formulation, the simplex method, duality, and network models (transportation, assignment) plus two-person zero-sum games. Expect small numerical LPs and duality checks.
303 words, about 2 min11Probability and Statistics
Probability and Statistics in GATE MA tests distributional calculations, limit theorems, estimation, and hypothesis testing. Problems often require deriving an MLE or applying the CLT with a continuity correction.
263 words, about 1 min